# Point A is at (2 ,-6 ) and point B is at (-2 ,-7 ). Point A is rotated (3pi)/2  clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

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Feb 22, 2018

Increase in distance due to rotation of A is $d = 9.8085$

#### Explanation:

$A \left(2 , - 6\right) , B \left(- 2 , - 7\right)$. Rotated about origin by $\frac{3 \pi}{2}$ clockwise.

$\vec{A B} = \sqrt{{\left(2 + 2\right)}^{2} + {\left(- 6 + 7\right)}^{2}} = 2.2361$

A((2),(-6)) -> A’((6),(2))

vec(A’B) = sqrt ((6+2)^2 + (2+7)^2) = 12.0416

Increase in distance due to rotation of A is

$d = 12.0416 - 2.2361 = 9.8085$

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